Transmission performance of long-haul optical communication systems such as transoceanic systems is limited by a number of phenomena, including amplified spontaneous emission (ASE) noise accumulation, dispersion, and a nonlinear component to the refractive index of the fiber. If the signal travels at the zero dispersion wavelength it will not suffer any temporal distortions. However, at the zero dispersion wavelength the signal and the ASE noise generated by the optical amplifiers travel at similar velocities (good phase matching) and thus have the opportunity to interact over long distances, via the Kerr effect. The result is the transfer of power out of the signal and into unwanted wavelengths.
Conversely if the signal propagates at a wavelength for which the dispersion is large then there is a large phase mismatch (group velocity difference) between the signal and noise, which greatly reduces the efficiency of four wave mixing. However, large values of dispersion result in increased inter-symbol interference due to the temporal spreading of the signal.
One of the most deleterious nonlinear interactions is known as modulation instability, which occurs for signal wavelengths that are less than about one nm greater than the zero dispersion wavelength. As a result of modulation instability, any fluctuations in the signal intensity caused by noise or dispersive effects that change the signal envelope shape will be enhanced by the Kerr effect through self phase modulation.
In known transmission systems dispersive and nonlinear distortions are simultaneously minimized by a dispersion management technique. One dispersion management technique is known as dispersion mapping, in which the zero dispersion wavelengths of the constituent fibers are chosen so that they are appropriately far from the system's operating wavelengths. Constituent fibers with different zero dispersion wavelengths are then arranged in some periodic fashion so that the path average dispersion for the whole transmission line is appropriately small. For example, the transmission line may be divided into two or more sections approximately equal length. In one section, the optical fiber has a zero dispersion wavelength less than the operating wavelengths. The following section has optical fiber with a zero dispersion wavelength greater than the operating wavelengths. The overall transmission line is thus constructed in a periodic manner from a concatenation of fiber sections having different zero dispersion wavelengths. By constructing the transmission line out of alternating lengths of positive and negative dispersion fiber, the path average dispersion can be adjusted so that it causes minimal temporal distortion. Moreover, by selecting the local dispersions of the constituent fibers to be large in magnitude, nonlinear interactions can be suppressed. Typically in dispersion managed systems the amount of positive and negative dispersion that is provided are equal to one another so that there is no net accumulated dispersion over the entire transmission line.
One factor complicating the dispersion map for a wavelength-division multiplexed transmission system is that optical fiber generally has a nonzero dispersion slope. That is, different wavelengths experience different dispersion values in a given fiber. As a result, in a WDM transmission system employing a plurality of wavelengths, the dispersion map can return the accumulated dispersion to zero for only one wavelength. All the other wavelengths will accumulate some net dispersion, which can be compensated on a channel by channel basis at the transmitter or receiver. As with a single channel system employing dispersion management, the net accumulated dispersion of the individual wavelengths in a WDM system is typically returned to zero.
Optimal or near optimal performance can be achieved by precise tailoring of the dispersion map to reduce nonlinear impairments for a given wavelength. In particular, it would be desirable to provide a dispersion map in which nonlinear penalties arising from self-phase modulation and the nonlinear interaction between the signal and ASE noise are reduced.